{"title":"Positive and sign-changing stationary solutions of degenerate logistic type equations","authors":"Maristela Cardoso , Flávia Furtado , Liliane Maia","doi":"10.1016/j.na.2024.113575","DOIUrl":null,"url":null,"abstract":"<div><p>In this work we study the existence and uniqueness of a positive, as well as a sign-changing steady-state solution of the degenerate logistic equation with a non-homogeneous superlinear term. Our outcome on a solution that changes sign, defined in higher dimensions, contribute to the existing literature of a few results for the problem, mostly developed in one dimension. We apply variational techniques, in particular the problem constrained to the Nehari manifold, and investigate how it changes as the parameter <span><math><mi>λ</mi></math></span> in the equation or the function <span><math><mi>b</mi></math></span> vary, affecting the existence and non-existence of solutions of the elliptic problem.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24000944","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this work we study the existence and uniqueness of a positive, as well as a sign-changing steady-state solution of the degenerate logistic equation with a non-homogeneous superlinear term. Our outcome on a solution that changes sign, defined in higher dimensions, contribute to the existing literature of a few results for the problem, mostly developed in one dimension. We apply variational techniques, in particular the problem constrained to the Nehari manifold, and investigate how it changes as the parameter in the equation or the function vary, affecting the existence and non-existence of solutions of the elliptic problem.
在这项工作中，我们研究了带有非均质超线性项的退化逻辑方程的正稳态解和符号变化稳态解的存在性和唯一性。我们关于在更高维度上定义的符号变化解的研究成果，为现有文献中关于该问题的一些结果做出了贡献，这些结果大多是在一维度上提出的。我们应用了变分技术，特别是约束在奈哈里流形上的问题，并研究了它如何随着方程中参数 λ 或函数 b 的变化而变化，从而影响椭圆问题解的存在与不存在。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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